Stability analysis of a fractional-order monkeypox epidemic model with quarantine and hospitalization

The monkeypox epidemic has become a global health issue due to its rapid transmission involving nonhuman-to-human transmission in nonendemic areas. Various actions, such as quarantine, vaccination, and hospitalization, have been implemented by worldwide governments. Given the relatively high cost and strict implementation of vaccination, our focus lies on quarantine and hospitalization. In this paper, we study the monkeypox epidemic involving quarantine and hospitalization through fractional-order mathematical modeling. The proposed model considers six classes of human populations (susceptible, exposed, infected, quarantined, hospitalized, and recovered) and three classes of nonhuman populations (susceptible, exposed, and infected). The basic properties of the model have been investigated, and its equilibrium points have been obtained, namely monkeypox-free, nonhuman-free endemic, and endemic. We have derived the basic reproduction numbers for human-to-human and nonhuman-to-nonhuman transmissions, denoted as $R_{0h}$ and $R_{0n}$ respectively. The existence and stability (both locally and globally) of each equilibrium point depend on $R_{0h}$ and $R_{0n}$ relative to unity. We performed calibration and forecasting of the model on the weekly monkeypox case data of the human population in the United States of America from June 1 to September 23, 2022. Research findings indicate that the fractional-order model shows better calibration and forecasting compared to the corresponding first-order model based on the root mean square error. Furthermore, the best-fitting model calibration indicates $R_0=\max \{R_{0h},R_{0n}\}>1$, suggesting the potential for endemic conditions in humans. However, the best forecasting shows $R_0<1$, possibly due to various policies such as vaccination. Given the relative cost and stringency of vaccination implementation for monkeypox control, we perform numerical simulations and sensitivity analyses on the basic reproduction number, particularly focusing on the impact of quarantine and hospitalization rates. Simulations and sensitivity analysis indicate that simultaneous increases in quarantine and hospitalization rates can reduce the basic reproduction number $R_{0h}$ below unity. Consequently, the monkeypox epidemic can be eradicated. Moreover, fractional-order derivative plays a crucial role in determining the spikes of monkeypox cases and the rapidity at which the disease undergoes either endemicity or extinction. Considerations of memory effects, quarantine, and hospitalization have a significant impact on monkeypox modeling studies, especially in capturing biological phenomena.